Drilled drains are installed in cases when the unfavorable groundwater regime is one of the main causes of slope instability. The time required for achieving the satisfactory factor of safety has to be calculated for effective application of drilled drains. The analysis of performance and effectiveness of drilled drains requires the application of 3D seepage models. The application of 3D models is, however, not practical due to their complexity in defining spatial relations in the slope and they are rarely used. As opposed to 3D models, 2D models can incorporate geometrical and material heterogeneities in vertical planes and they are relatively simple to use and apply. The research on this topic has examined the possibility of the application of 2D models in cases of slopes with installed drilled drains. The applicability of this solution for the calculation of the increase of slope stability with time was also examined. The research results enabled us to define a procedure for analyzing the influence of drilled drains on the increase of slope stability with time with the use of 2D models with the appropriate selection of equivalent drain permeability.